You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?
A. 50 mph
B. 20 mph
C. 10 mph
D. 60 mph
To find the average speed, we divide the total distance traveled by the total time taken.
For the first route, the average speed is given by: 400 miles / 8 hours = 50 mph.
For the second route, the average speed is given by: 420 miles / 7 hours = 60 mph.
Therefore, the average speed on the faster route is 60 mph, and the average speed on the slower route is 50 mph.
The difference between the two average speeds is therefore 60 mph - 50 mph = 10 mph.
Therefore, the correct answer is C. 10 mph.
To determine the average speed, we need to calculate the rate of speed (miles per hour) for each route.
Let's start with the first route, which is 400 miles in 8 hours. We can write an equation to calculate the average speed (S1) for this route:
S1 = 400 miles / 8 hours
Simplifying this equation gives us:
S1 = 50 miles/hour
Next, let's consider the second route, which is 420 miles in 7 hours. We can write an equation to determine the average speed (S2) for this route:
S2 = 420 miles / 7 hours
Simplifying this equation gives us:
S2 = 60 miles/hour
To find the difference in average speeds between the two routes, we subtract the average speed of the first route from the average speed of the second route:
S2 - S1 = 60 miles/hour - 50 miles/hour
Simplifying this equation gives us:
S2 - S1 = 10 miles/hour
Therefore, the difference in average speed between the two routes is 10 miles per hour. So, the correct answer is:
C. 10 mph
To find the average speed, we divide the distance by the time.
For the first route:
Average speed = 400 miles / 8 hours = 50 mph
For the second route:
Average speed = 420 miles / 7 hours = 60 mph
The difference between the two average speeds is 60 mph - 50 mph = 10 mph.
Therefore, the correct answer is C. 10 mph.